Get Math Help

Home / Get Math Help

Champernowne Constant Continued Fraction

Continued fraction

[0; 8, 9, 1, 149083, 1, 1, 1, 4, 1, 1, 1, 3, 4, 1, 1, 1, 15, 457540111391031076483, ...]

Continued fraction representations

$tanh(1) = continued fraction k _(k=1)^∞ 1/(2 k - 1)$

$sqrt(5) = 1 + 2 continued fraction k _(k=1)^∞ 1/1$

$sqrt(2) = 1 + continued fraction k _(k=1)^∞ 1/2$

$sqrt((e π)/2) erfc(1/sqrt(2)) = 1/(1 + continued fraction k _(k=1)^∞ k/1)$

$log(2) = 1/(1 + continued fraction k _(k=1)^∞ k^2/1)$

$ζ(2) = 2/(1 + continued fraction k _(k=1)^∞ k^4/(2 k + 1))$

$log(2) = 2/(3 + continued fraction k _(k=1)^∞ (-k^2)/((2 k + 1) 3))$

$2^(1/3) = 1 + 2/(8 + continued fraction k _(k=1)^∞ (1 - 9 k^2)/(9 (1 + 2 k)))$

$polygamma(2, 2) = -2/(5 + continued fraction k _(k=1)^∞ (-k^6)/((2 k + 1) (5 + k + k^2)))$

$ζ(3) = 1 + 1/(5 + continued fraction k _(k=1)^∞ (-k^6)/((2 k + 1) (5 + k + k^2)))$